Our motivation to study the cohomology theory of a Borel dynamical system stems from the fact that a similar study in ergodic theory and topological dynamics has proved to be very useful. Cohomology theory has been used in the study of measure-theoretic dynamical systems up to orbit equivalence. It has given rise to methods that have been widely applied in the classification of dynamical systems. A complete reference to papers focused on the study of cohomology in this context is too long to mention. We list few key reference which include the seminal work of Ramsay [1]}, Moore [2]}, Schmidt [3]}, [4]} and Zimmer [5]}.
